I do not believe that any questions in scope for this site begin with "Why" or "How"; this community has limited itself to "Who", "What", and "When" questions.
I think we could reduce the likelihood of a bad question being asked by either prompting users with our FAQ when they try to ask a "why" or "how" question or by outright disallowing such questions.
Is this a worthwhile endeavor?
I had a very similar idea about a year ago. I was wondering if questions that started with Who, What, When, Where, How, Why, or Which were "general knowledge" questions, and might be automatically rejected. (This is a broader set than your suggestion.)
I did some quick experiment, which I documented here:
Can the quality of a question be judged by the first word in the title?
My conclusion was: As expected, they generally fared worse (on votes and rate of closure) than questions that started with Is, Are, Was, Were, Do, Does, Can, Has, Have or Did. However, the difference wasn't so stark that a blanket ban or other measure could be reasonably considered.
In short: I agree with the idea in principle, but the data only supported it weakly, not strongly.
(Notwithstanding that the effect might be much stronger if you limit it to only "Why" and "How".)
I thought about it some time back. The thing is, most "why" questions can be rephrased not to use it and not all why questions are actually unfeasible (some just have bad titles). So such a specific criterion is probably not totally useful.
We do disallow questions about "motivations" which already disallows the worse of the "why" questions.
